My coat has three buttons. How many ways can you find to do up all the buttons?

In this maze of hexagons, you start in the centre at 0. The next hexagon must be a multiple of 2 and the next a multiple of 5. What are the possible paths you could take?

My briefcase has a three-number combination lock, but I have forgotten the combination. I remember that there's a 3, a 5 and an 8. How many possible combinations are there to try?

Imagine that the puzzle pieces of a jigsaw are roughly a rectangular shape and all the same size. How many different puzzle pieces could there be?

The Red Express Train usually has five red carriages. How many ways can you find to add two blue carriages?

Lorenzie was packing his bag for a school trip. He packed four shirts and three pairs of pants. "I will be able to have a different outfit each day", he said. How many days will Lorenzie be away?

These activities focus on finding all possible solutions so if you work in a systematic way, you won't leave any out.

Seven friends went to a fun fair with lots of scary rides. They decided to pair up for rides until each friend had ridden once with each of the others. What was the total number rides?

These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.

Using the statements, can you work out how many of each type of rabbit there are in these pens?

El Crico the cricket has to cross a square patio to get home. He can jump the length of one tile, two tiles and three tiles. Can you find a path that would get El Crico home in three jumps?

Start with three pairs of socks. Now mix them up so that no mismatched pair is the same as another mismatched pair. Is there more than one way to do it?

The Vikings communicated in writing by making simple scratches on wood or stones called runes. Can you work out how their code works using the table of the alphabet?

Moira is late for school. What is the shortest route she can take from the school gates to the entrance?

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.

A merchant brings four bars of gold to a jeweller. How can the jeweller use the scales just twice to identify the lighter, fake bar?

The challenge here is to find as many routes as you can for a fence to go so that this town is divided up into two halves, each with 8 blocks.

If these elves wear a different outfit every day for as many days as possible, how many days can their fun last?

How many different shapes can you make by putting four right- angled isosceles triangles together?

If we had 16 light bars which digital numbers could we make? How will you know you've found them all?

Use the clues to work out which cities Mohamed, Sheng, Tanya and Bharat live in.

When newspaper pages get separated at home we have to try to sort them out and get things in the correct order. How many ways can we arrange these pages so that the numbering may be different?

Chandra, Jane, Terry and Harry ordered their lunches from the sandwich shop. Use the information below to find out who ordered each sandwich.

Can you find out in which order the children are standing in this line?

Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?

Use the information to describe these marbles. What colours must be on marbles that sparkle when rolling but are dark inside?

What is the smallest number of jumps needed before the white rabbits and the grey rabbits can continue along their path?

Can you find all the ways to get 15 at the top of this triangle of numbers?

Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.

This task follows on from Build it Up and takes the ideas into three dimensions!

The Zargoes use almost the same alphabet as English. What does this birthday message say?

Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?

This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.

Six friends sat around a circular table. Can you work out from the information who sat where and what their profession were?

Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.

Winifred Wytsh bought a box each of jelly babies, milk jelly bears, yellow jelly bees and jelly belly beans. In how many different ways could she make a jolly jelly feast with 32 legs?

Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.

Sitting around a table are three girls and three boys. Use the clues to work out were each person is sitting.

Ana and Ross looked in a trunk in the attic. They found old cloaks and gowns, hats and masks. How many possible costumes could they make?

These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.

These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.

This challenge focuses on finding the sum and difference of pairs of two-digit numbers.

Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?

If you have three circular objects, you could arrange them so that they are separate, touching, overlapping or inside each other. Can you investigate all the different possibilities?

These activities focus on finding all possible solutions so if you work in a systematic way, you won't leave any out.